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EEC202 – Advanced Digital Signal Processing

4 units – Spring Quarter; alternate years

Lecture: 4 hours

Prerequisite: EEC 201; EEC 260, EEC 265, and MAT 167 are recommended.

Grading: Letter; homework (50%); course project (50%).

Catalog Description:

Multirate DSP theory and wavelets, optimal transform and subband coders in data compressions, advanced sampling theory and oversampled A/D converters, transmultiplexers and precoders in digital communication systems, genomic signal processing.

Expanded Course Description:

This class covers advanced Digital Signal Processing (DSP) concepts that play a key role in state of the art technologies. Specifically, we first introduce the theory of multirate DSP such as decimators, interpolators, delay chains, blocking/unblocking operators, decimation and interpolation filters, the polyphase representation and perfect reconstruction filter banks. We also study lossless systems, linear periodically time varying systems, time-frequency representations and wavelets. We then discuss a number of related research topics such as transform and subband coding in data compression, advanced sampling theory in oversampled A/D converters, transmultiplexers and precoders in broadband wireline communication systems (e.g. xDSL systems), fractionally spaced and non-uniformly spaced equalizers in digital communications and, (multirate) DSP and wavelet applications in genomics signal processing. The course has the dual role of presenting advanced DSP tools to the general class body while preparing the more specialized student for pursuing research in the DSP area.

  1. Multirate DSP Basics
    1. Introduction, motivation and historical perspective
    2. The decimator: time and frequency domain analysis
    3. The upsampler: time and frequency domain analysis
    4. Fractional sampling rate and application in digital audio
    5. Decimation and interpolation filters
    6. Interconnection of multirate building blocks and the noble identities
  2. The Polyphase Representation
    1. Blocking and unblocking operators
    2. Type I and Type II polyphase decomposition
    3. Efficient structures for decimation and interpolation filters
    4. The polyphase identity
    5. Application in digital filter design: the interpolated FIR approach
  3. Special Filters and Filter Banks
    1. The uniform DFT filter bank
    2. The decimated DFT filter bank and its polyphase representation
    3. Perfect reconstruction property of the DFT filter bank
    4. Nyquist(M) filters, power complementary filters and, Euclidian complementary filters
  4. Maximally Decimated Filter Banks
    1. Errors in a filter bank structure
    2. M-channel filter bank and its polyphase representation
    3. Perfect reconstruction filter banks with examples
    4. Alias free filter banks with examples
    5. Uniform tree structured filter banks
  5. Paraunitary Perfect Reconstruction Filter Banks
    1. Lossless transfer matrices
    2. Properties of paraunitary filter banks
    3. Two and M-channel FIR paraunitary filter banks
    4. The paraunitary lattice structure
    5. The lapped orthogonal transform
  6. Special Topics
    1. Block filters and linear periodically time-varying (LPTV) systems
    2. Short-time Fourier transform and the wavelet transform
    3. Discrete-time orthonormal wavelets
  7. Applications in Data Compression
    1. Quantization of subband signals and noise models
    2. Optimal transform coders: the KLT and DCT
  8. Applications in A/D Converters
    1. Advanced sampling theory
    2. Oversampled A/D conversion techniques
  9. Applications in OFDM systems
    1. Transmultiplexers and perfect reconstruction conditions
    2. Application in multi-carrier modulation: the DMT system
  10. Applications in Channel Equalization
    1. Fractionally spaced equalizers
    2. Non uniformly spaced equalizers
  11. Applications in Genomic Signal Processing

Statement of Course Design Project:

The students are first introduced to the theory of multirate DSP, lossless systems, linear periodically time-varying systems, time frequency representations and wavelets. They are then exposed to a number of contemporary DSP applications from data compression to communication system design to genomic signal processing where the above theoretical concepts and design tools play an essential role in the corresponding application. In the course project, students are in turn encouraged to explore novel research directions by either modifying previous work or studying new emerging applications. The course project is considered a research training activity where the students are expected to use their acquired knowledge and developed expertise in the field of (digital) signal processing to study in depth a particular DSP subject of their choice. Through outside reading and critical understanding of published technical papers, students will learn how to formulate a research problem and develop an approach towards its solution. Students are required to work alone, must submit a project report summarizing their findings by the end of the term and finally describe their work to the rest of the class through a short oral presentation.

ABET Category Content:

Engineering Science: 2 credits

Engineering Design: 2 credits

Textbook/reading:

  1. Multirate Systems and Filter Banks by P.P. Vaidyanathan, Prentice Hall, Upper Saddle River, new Jersey, 1993.
  2. Lecture notes and technical papers.

Instructor: Tuqan

Course Overlap:

Although fractionally spaced equalizers are discussed in EEC 261 and transform coders are introduced in EEC 209, the exposition of these topics here is based solely on a multirate DSP perspective which is fundamentally different from the approach adopted in the other two classes. We therefore believe that there is minimal overalp with EEC 261 and EEC 209.

Last revised: March 2006